Sequences

3,043 sequences

• A145324 → basis A013611
  1 · 3, 8 · 12, 68, 96 · 60, 532, 1568, 1536 … row sums 1, 11, 176, 3696, 96096, 2978976, …
  (−∞, 0] nonnegative rational roots
• A081580 → D
  1 · 7, 2 · 13, 26, 3 · 19, 122, 57, 4 … row sums 0, 1, 9, 42, 202, 855, 3567, 14308, …
  (−∞, 0] nonnegative
• A143494 → (θ+1)²
  1 · 2, 4 · 4, 20, 9 · 8, 76, 81, 16 … row sums 1, 6, 33, 181, 1020, 5977, 36589, …
  (−∞, 0] nonnegative
• A063967 → x ↦ x−4
  1 · -3, 1 · 6, -5, 1 · -9, 15, -7, 1 … row sums 1, -2, 2, 0, -4, 8, -8, 0, …
  (−1, 3]
• A391533 → basis A013609
  9, 12, 4 · 18, 42, 32, 8 · 36, 120, 148, 80, 16 … row sums 25, 100, 400, 1600, 6400, 25600, …
  (−∞, 0] nonnegative rational roots
• A145324: Triangle read by rows: coefficients of 1; 1(X+2); 1(X+2)(X+3); 1(X+2)(X+3)(X+4); ....
  1 · 1, 2 · 1, 5, 6 · 1, 9, 26, 24 … row sums 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  A145324 (−∞, 0) [−1, 0] nonnegative rational roots
• A064861 → D
  3, 4 · 5, 16, 12 · 6, 26, 36, 16 … row sums 7, 33, 84, 324, 756, 2700, 6048, 20736, …
  (−∞, 0] nonnegative rational roots
• A200536 → basis A013610
  1 · 6, 21, 18 · 36, 252, 657, 756, 324 … row sums 1, 45, 2025, 91125, 4100625, 184528125, …
  (−∞, 0] nonnegative rational roots
• A121574 → D+1
  1 · 3, 1 · 9, 7, 1 · 24, 32, 11, 1 … row sums 1, 4, 17, 68, 264, 1002, 3739, 13768, …
  (−∞, 0] nonnegative
• A062145 → θ+1
  1 · 1, 8 · 1, 20, 30 · 1, 36, 135, 80 … row sums 1, 9, 51, 252, 1170, 5247, 23023, …
  (−∞, 0] nonnegative
• A063967 → reverse
  1 · 1, 1 · 1, 3, 2 · 1, 5, 7, 3 … row sums 1, 2, 6, 16, 44, 120, 328, 896, …
  (−∞, 0] nonnegative
• A113214 → basis A013609
  1 · 3, 2 · 4, 10, 4 · 7, 26, 28, 8 … row sums 1, 5, 18, 69, 261, 990, 3753, 14229, …
  (−∞, 0] nonnegative
• A008292 → γ (scale 1/4) (shift +1) → x ↦ x+1
  1 · 2 · 6, 2 · 24, 16 … row sums 1, 2, 8, 40, 256, 1952, 17408, 177280, …
  (−∞, −1] nonnegative
• A132393 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 6, 22, 24, 8 … row sums 1, 3, 12, 60, 360, 2520, 20160, 181440, …
  (−∞, 0] nonnegative rational roots
• A039755 → D+1
  1 · 2, 1 · 5, 6, 1 · 14, 31, 12, 1 … row sums 1, 3, 12, 58, 324, 2044, 14320, 109960, …
  (−∞, 0] nonnegative
• basis-map coefficients of A021012 → Veronese 2
  1 · 0, 2 · 0, 0, 24 · 0, 0, 0, 720 … row sums 1, 0, 2, 0, 24, 0, 720, 0, …
  (−∞, 0] nonnegative rational roots
• A216973: Exponential Riordan array [x*exp(x),x].
  A007318 → D
  1 · 2, 2 · 3, 6, 3 · 4, 12, 12, 4 … row sums 0, 1, 4, 12, 32, 80, 192, 448, …
  A216973 (−∞, −1] nonnegative rational roots
• A172431 → Veronese 2 (j=1)
  2 · 4 · 6, 4 · 8, 20 … row sums 0, 2, 4, 10, 28, 72, 188, 494, …
  (−∞, 0] nonnegative
• A128813 → basis A008277
  1 · 2, 1 · 8, 13, 3 · 56, 217, 135, 18 … row sums 1, 3, 24, 426, 14356, 817201, 72259579, …
  (−∞, 0] nonnegative
• A207823: Triangle of coefficients of Chebyshev's S(n,x+4) polynomials (exponents of x in increasing order).
  1 · 4, 1 · 15, 8, 1 · 56, 46, 12, 1 … row sums 1, 5, 24, 115, 551, 2640, 12649, 60605, …
  A207823 (−6, −2) nonnegative
• A126351 → D
  2 · 5, 8 · 9, 38, 24 · 14, 110, 195, 64 … row sums 0, 2, 13, 71, 383, 2129, 12360, 75242, …
  (−∞, 0] nonnegative
• A007318 → ×(−(1/2)n+(1/2)n²) → D+1
  3, 4, 1 · 12, 27, 18, 3 · 30, 96, 108, 48, 6 … row sums 0, 0, 8, 60, 288, 1120, 3840, 12096, …
  (−∞, 0] nonnegative rational roots
• A102662 → D
  3 · 5, 6 · 7, 22, 9 · 9, 46, 51, 12 … row sums 0, 3, 11, 38, 118, 349, 997, 2780, …
  (−∞, 0] nonnegative
• A137338 → D+1
  1 · 0, 1 · -3, -1, 1 · 9, -6, -3, 1 … row sums 1, 1, -3, 1, 13, -61, 223, -867, …
  (−∞, ∞)
• A013618 → basis A013611
  144, 1056, 1936 · 1728, 19008, 69696, 85184 … row sums 3136, 175616, 9834496, 550731776, …
  (−∞, 0] nonnegative rational roots
• A282629: Sheffer triangle (exp(x), exp(3*x) - 1). Named S2[3,1].
  1 · 1, 3 · 1, 15, 9 · 1, 63, 108, 27 … row sums 1, 4, 25, 199, 1876, 20257, 245017, …
  A282629 (−∞, 0) nonnegative
• A128099 → Veronese 2 (j=1)
  2 · 4 · 6 · 8 … row sums 0, 0, 2, 4, 6, 8, 18, 44, …
  (−∞, 0] nonnegative
• A225470 → Pₙ + Pₙ₊₁
  3, 1 · 12, 8, 1 · 90, 73, 16, 1 … row sums 4, 21, 180, 2106, 31104, 554040, …
  (−∞, ∞) nonnegative rational roots
• A116414 → basis A007318
  1 · 5, 1 · 22, 10, 1 · 95, 69, 15, 1 … row sums 1, 6, 33, 180, 981, 5346, 29133, …
  (−9, −1) nonnegative
• A113214 → x ↦ x−2
  1 · 0, 1 · -2, -1, 1 · 4, -2, -2, 1 … row sums 1, 1, -2, 1, 1, -2, 1, 1, …
  (−2, 2]
• A111125: Triangle read by rows: T(k,s) = ((2*k+1)/(2*s+1))*binomial(k+s,2*s), 0 <= s <= k.
  1 · 3, 1 · 5, 5, 1 · 7, 14, 7, 1 … row sums 1, 4, 11, 29, 76, 199, 521, 1364, …
  A111125 (−4, 0) nonnegative
• A249250 → D
  3 · 6, 6 · 9, 30, 9 · 12, 72, 72, 12 … row sums 0, 3, 12, 48, 168, 564, 1824, 5760, …
  (−∞, 0] nonnegative
• A013612 → basis A013610
  36, 180, 225 · 216, 1620, 4050, 3375 … row sums 441, 9261, 194481, 4084101, 85766121, …
  (−∞, 0] nonnegative rational roots
• A038303 → basis A007318
  1 · 11, 1 · 121, 22, 1 · 1331, 363, 33, 1 … row sums 1, 12, 144, 1728, 20736, 248832, …
  (−∞, 0] nonnegative rational roots
• A038328 → basis A013609
  196, 112, 16 · 2744, 2352, 672, 64 … row sums 324, 5832, 104976, 1889568, 34012224, …
  (−∞, 0] nonnegative rational roots
• A139548 → basis A013609
  1 · 8, 16, 8 · 64, 256, 384, 256, 64 … row sums 1, 32, 1024, 32768, 1048576, 33554432, …
  (−∞, 0] nonnegative rational roots
• A008288 → D
  1 · 3, 2 · 5, 10, 3 · 7, 26, 21, 4 … row sums 0, 1, 5, 18, 58, 175, 507, 1428, …
  (−∞, 0] nonnegative
• A269944 → basis A013609
  1 · 1, 2 · 2, 6, 4 · 10, 34, 32, 8 … row sums 1, 3, 12, 84, 1008, 19152, 536256, …
  (−∞, 0] nonnegative rational roots
• A027467 → basis A013609
  1 · 16, 2 · 256, 64, 4 · 4096, 1536, 192, 8 … row sums 1, 18, 324, 5832, 104976, 1889568, …
  (−∞, 0] nonnegative rational roots
• A094816: Triangle read by rows: T(n,k) are the coefficients of Charlier polynomials: A046716 transposed, for 0 <= k <= n.
  1 · 1, 1 · 1, 3, 1 · 1, 8, 6, 1 … row sums 1, 2, 5, 16, 65, 326, 1957, 13700, …
  A094816 (−∞, 0) nonnegative
• A347056: Triangle read by rows: T(n,k) = (n+1)*(n+2)*(k+3)*binomial(n,k)/6, 0 <= k <= n.
  A007318 → (1/3+(1/2)n+(1/6)n²)θ+1+(3/2)n+(1/2)n²
  1 · 3, 4 · 6, 16, 10 · 10, 40, 50, 20 … row sums 1, 7, 32, 120, 400, 1232, 3584, 9984, …
  A347056 (−∞, 0] nonnegative rational roots
• A344565 → x ↦ x/(x+1)
  3 · 15, 30 · 45, 180, 180 · 105, 630, 1260, 840 … row sums 3, 45, 405, 2835, 17010, 91854, 459270, …
  [−1, 0] nonnegative rational roots
• A113953 → basis A013611
  1 · 1, 4 · 3, 16, 16 · 5, 44, 112, 64 … row sums 1, 5, 35, 225, 1475, 9625, 62875, …
  (−∞, 0] nonnegative
• A038330 → basis A008277
  256, 144, 16 · 4096, 3904, 960, 64 … row sums 416, 9024, 204544, 4849664, 120303616, …
  (−∞, 0] nonnegative
• A142462 → Pₙ + Pₙ₊₁
  2, 1 · 2, 17, 1 · 2, 159, 144, 1 … row sums 3, 20, 306, 6912, 205344, 7551360, …
  (−∞, ∞) nonnegative
• A038321 → basis A007318
  324, 252, 49 · 5832, 6804, 2646, 343 … row sums 625, 15625, 390625, 9765625, 244140625, …
  (−∞, 0] nonnegative rational roots
• A007318 → θ+1 → x ↦ x+1
  1 · 3, 2 · 8, 10, 3 · 20, 36, 21, 4 … row sums 1, 5, 21, 81, 297, 1053, 3645, 12393, …
  (−∞, −1] nonnegative rational roots
• A001263 → basis A013611
  1 · 2, 4 · 5, 20, 16 · 14, 84, 144, 64 … row sums 1, 6, 41, 306, 2426, 20076, 171481, …
  (−∞, 0] nonnegative
• A139548: Triangle T(n,k) with the coefficient of [x^k] of the polynomial (2*(x+1)^2)^n in row n, column k, 0<=k<=2n.
  1 · 2, 4, 2 · 4, 16, 24, 16, 4 … row sums 1, 8, 64, 512, 4096, 32768, 262144, …
  A139548 (−∞, 0] nonnegative rational roots
• A013609 → basis A008288
  1 · 3, 2 · 9, 16, 4 · 27, 82, 52, 8 … row sums 1, 5, 29, 169, 985, 5741, 33461, …
  [−3−2√2, −3+2√2] nonnegative